While getting to inbox zero doesn't have to suck, it still requires effort. That effort starts to seem endless when people reply to every email you send while you're still making your way through. Rory Vaden, writing for Fast Company, recommends going offline to solve this problem:

Do not underestimate the power of momentum when responding to emails. Nothing is more emotionally defeating than spending 2 hours in your inbox and having a net gain of only 2 emails completed because responses were coming in as fast as you were sending them out or because you got into a game of "email tennis" with someone who obviously has more time on their hands than you do. Instead, work "offline" every single time you answer emails. That way you can focus on what you are doing and you can capitalize on the synergy that comes along with getting into a rhythm of responding.

While this won't necessarily work so well if you spend most of your time in a webmail client, most desktop mail apps offer an offline mode. Find it, turn it on, and start replying. When you go back online, the app will send your messages and you won't have to worry about constant replies.